Inverse turbulent cascades and conformally invariant curves

We offer a new example of conformal invariance far from equilibrium -- the inverse cascade of Surface Quasi-Geostrophic (SQG) turbulence. We show that temperature isolines are statistically equivalent to curves that can be mapped into a one-dimensional Brownian walk (called Schramm-Loewner Evolution or SLE$_\kappa$). The diffusivity is close to $\kappa=4$, that is iso-temperature curves belong to the same universality class as domain walls in the O(2) spin model. Several statistics of temperature clusters and isolines are measured and shown to be consistent with the theoretical expectations for such a spin system at criticality. We also show that the direct cascade in two-dimensional Navier-Stokes turbulence is not conformal invariant. The emerging picture is that conformal invariance may be expected for inverse turbulent cascades of strongly interacting systems.Comment: 4 pages, 6 figure

Three-point correlation function of a scalar mixed by an almost smooth random velocity field

We demonstrate that if the exponent $\gamma$ that measures non-smoothness of the velocity field is small then the isotropic zero modes of the scalar's triple correlation function have the scaling exponents proportional to $\sqrt{\gamma}$. Therefore, zero modes are subleading with respect to the forced solution that has normal scaling with the exponent $\gamma$.Comment: 13 pages, RevTeX 3.

Statistics of interacting optical solitons

We examine statistics of two interacting optical solitons and describe timing jitter caused by spontaneous emission noise and enhanced by pulse interaction. Dynamics of phase difference is shown to be of crucial importance in determining the probability distribution function (PDF) of the distance between solitons. We find analytically the non-Gaussian tail of the PDF to be exponential. The propagation distance that corresponds to a given bit-error rate is described as a function of system parameters (filtering and noise level), initial distance, and initial phase difference between solitons. We find the interval of parameters where a larger propagation distance can be achieved for higher density of information

Single-point velocity distribution in turbulence

We show that the tails of the single-point velocity probability distribution function (PDF) are generally non-Gaussian in developed turbulence. By using instanton formalism for the Navier-Stokes equation, we establish the relation between the PDF tails of the velocity and those of the external forcing. In particular, we show that a Gaussian random force having correlation scale $L$ and correlation time $\tau$ produces velocity PDF tails $\ln{\cal P}(v)\propto-v^4$ at $v\gg v_{rms}, L/\tau$. For a short-correlated forcing when $\tau\ll L/v_{rms}$ there is an intermediate asymptotics $\ln {\cal P}(v)\propto-v^3$ at $L/\tau\gg v\gg v_{rms}$.Comment: 9 pages, revtex, no figure

Conformal invariance in two-dimensional turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often demonstrate symmetries, in particular scale invariance. In two dimensions (2d) locality often promotes scale invariance to a wider class of conformal transformations which allow for nonuniform re-scaling. Conformal invariance allows a thorough classification of universality classes of critical phenomena in 2d. Is there conformal invariance in 2d turbulence, a paradigmatic example of strongly-interacting non-equilibrium system? Here, using numerical experiment, we show that some features of 2d inverse turbulent cascade display conformal invariance. We observe that the statistics of vorticity clusters is remarkably close to that of critical percolation, one of the simplest universality classes of critical phenomena. These results represent a new step in the unification of 2d physics within the framework of conformal symmetry.Comment: 10 pages, 5 figures, 1 tabl

Statistics of soliton-bearing systems with additive noise

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a further development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governing by noisy Nonlinear Schr\"odinger Equation (NSE). We then apply our method to optical soliton transmission systems using signal control elements (filters, amplitude and phase modulators).Comment: 4 pages. Submitted to PR

Nonlinear interaction between long inertio-gravity and rossby waves

International audienceThe equations describing the interaction of long inertio-gravity (IG) waves with the Rossby waves are derived. Due to remarkable cancellations, the interaction is shown to be anomalously weak. As a result, an inverse cascade of turbulence produces wave condensate of large amplitude so that wave breaking with front creation can occur